Solve v^2+xv=2u

$$v ^ { 2 } + x v = 2 u$$

Solve for u

$$u=\frac{v\left(x+v\right)}{2}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2u=v^{2}+xv$$

The equation is in standard form.

$$2u=vx+v^{2}$$

Divide both sides by 2.

$$\frac{2u}{2}=\frac{v\left(x+v\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$u=\frac{v\left(x+v\right)}{2}$$

Solve for v (complex solution)

$$v=\frac{\sqrt{x^{2}+8u}-x}{2}$$

$$v=\frac{-\sqrt{x^{2}+8u}-x}{2}$$

Solve for v

$$v=\frac{\sqrt{x^{2}+8u}-x}{2}$$

$$v=\frac{-\sqrt{x^{2}+8u}-x}{2}\text{, }u\geq -\frac{x^{2}}{8}$$